A word to describe indiscretion people

The two parts of your question are opposites. Do you mean a word for people who cannot maintain discretion?

How about "indiscreet"?

Yes you are correct.
But "indiscreet" seems more formal.
I guess it should be something like "His mouth is too open and he would throw out everything from his heart".

Are they unable to hide the truth of what they're doing from others—e.g. failing to conceal a clandestine affair—or do they often say things that would be better left unsaid? The former would indicate a lack of discretion, in which case indiscreet seems fitting, whereas the latter would probably best be described as tactless.

Thank you Mr. Wordy and Falconer again.

I guess "tactless" is appropriate in my case.

Anyway, I also wonder what "they are doing from others" means. Google too hits many results for the expression.

He's a blabbermouth.

He can't keep a secret.

He's got no filter. Whatever is in his head comes out his mouth.

User_garyI also wonder what "they are doing from others" means.

You're parsing it wrong. hide goes with from.

hide
what they are doing / their actions / the truth about their actions

from other people

CJ

Thanks a lot Grammargreek

I was exactly looking for what you have written here.

Thanks to CalifJim as well.
Now I got it. English is so tough after all.